Paper 15 in the Non-Holomorphic Fractal Series. Paper 11 reported three numerical anchor values for the Class A Stokes constant S₁ᴬ (α) at α ∈ 1/4, 1/2, 3/4, extracted via a Definition 4. 1 amplitude ratio on the Stokes ray. These values, together with the sign result of Paper 12 and the α^1/3 power law of Paper 14, formed the empirical backbone of the series. Subsequent exhaustive experiments showed that no implementation faithful to the finalized Watson–boundary-layer–Picard–Lefschetz (Watson–BL–PL) framework reproduces the anchors. Every spec-true realization of the area law, Watson factor, BL series and normalization either drives the Definition 4. 1 ratio to 0 or to a large K-independent constant f (α) ≫ 1, never to the legacy triple (0. 59612, 0. 76328, 0. 89320). This paper formalizes that impossibility as two structural theorems, one for the analytic Watson area law and one for pixel-count fractal areas with Watson scaling, and proves a forensic provenance lemma reclassifying the anchors as legacy empirical constants. In their place we introduce a reproducible Picard–Lefschetz definition of the Class A Stokes constant via the endpoint half-thimble integral, consistent with the sign from Paper 12 and the α^1/3 exponent from Paper 14. This new definition is the foundation for the numerical Picard–Lefschetz law in Paper 16.
Michael Bird (Sat,) studied this question.